| Label |
Class |
Conductor |
Discriminant |
Rank* |
2-Selmer rank |
Torsion |
$\textrm{End}^0(J_{\overline\Q})$ |
$\textrm{End}^0(J)$ |
$\GL_2\textsf{-type}$ |
Sato-Tate |
Nonmaximal primes |
$\Q$-simple |
\(\overline{\Q}\)-simple |
\(\Aut(X)\) |
\(\Aut(X_{\overline{\Q}})\) |
$\Q$-points |
$\Q$-Weierstrass points |
mod-$\ell$ images |
Locally solvable |
Square Ш* |
Analytic Ш* |
Tamagawa |
Regulator |
Real period |
Leading coefficient |
Igusa-Clebsch invariants |
Igusa invariants |
G2-invariants |
Equation |
| 20736.a.20736.1 |
20736.a |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.960.8 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.923707\) |
\(0.932732\) |
$[78,216,4806,81]$ |
$[156,438,-428,-64653,20736]$ |
$[4455516,160381/2,-18083/36]$ |
$y^2 = x^5 + x^4 - 3x^3 - 4x^2 - x$ |
| 20736.b.41472.1 |
20736.b |
\( 2^{8} \cdot 3^{4} \) |
\( - 2^{9} \cdot 3^{4} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.267344\) |
\(9.961974\) |
\(1.331635\) |
$[150,-378,-12744,-162]$ |
$[300,4758,69124,-475341,-41472]$ |
$[-58593750,-12390625/4,-10800625/72]$ |
$y^2 + y = 2x^5 - 3x^4 - x^3 + 3x^2 - 1$ |
| 20736.c.41472.1 |
20736.c |
\( 2^{8} \cdot 3^{4} \) |
\( - 2^{9} \cdot 3^{4} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.40.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.022947\) |
\(18.286094\) |
\(1.258813\) |
$[72,225,5031,162]$ |
$[144,264,-4864,-192528,41472]$ |
$[1492992,19008,-2432]$ |
$y^2 + x^3y = -x^4 + 3x^2 - 4x + 2$ |
| 20736.d.41472.1 |
20736.d |
\( 2^{8} \cdot 3^{4} \) |
\( - 2^{9} \cdot 3^{4} \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1, 3.80.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(10.483302\) |
\(1.310413\) |
$[1392,-459,-212895,-162]$ |
$[2784,324168,50516032,8887935216,-41472]$ |
$[-4032655982592,-168664178176,-84967965824/9]$ |
$y^2 + y = 6x^6 - 6x^4 - 2x^3 + 3x^2 + x - 1$ |
| 20736.e.82944.1 |
20736.e |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{4} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.120.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.385807\) |
\(1.346452\) |
$[42,1080,3852,-324]$ |
$[84,-2586,41180,-807069,-82944]$ |
$[-50421,147833/8,-504455/144]$ |
$y^2 = x^5 + x^4 + x^3 - 2x^2 - 2x - 2$ |
| 20736.f.186624.1 |
20736.f |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{6} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.834469\) |
\(1.468963\) |
$[74,288,5502,3]$ |
$[444,1302,-1292,-567213,186624]$ |
$[277375828/3,10991701/18,-442187/324]$ |
$y^2 = x^5 - 2x^4 - 9x^3 - 7x^2 - x$ |
| 20736.g.186624.1 |
20736.g |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{6} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.153445\) |
\(1.322090\) |
$[74,288,5502,3]$ |
$[444,1302,-1292,-567213,186624]$ |
$[277375828/3,10991701/18,-442187/324]$ |
$y^2 = x^5 + 2x^4 - 9x^3 + 7x^2 - x$ |
| 20736.h.331776.1 |
20736.h |
\( 2^{8} \cdot 3^{4} \) |
\( - 2^{12} \cdot 3^{4} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.112729\) |
\(6.735253\) |
\(1.518522\) |
$[1284,-2178,-988758,-41472]$ |
$[1284,70146,5261188,458726019,-331776]$ |
$[-42076551921/4,-14321977713/32,-15058835353/576]$ |
$y^2 + x^2y = x^6 - 3x^5 + 5x^3 - 3x^2 + 2x - 3$ |
| 20736.i.373248.1 |
20736.i |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{6} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\mathsf{CM})\) |
\(\Q \times \Q\) |
✓ |
$D_{2,1}$ |
|
|
|
$C_2^2$ |
$C_3:D_4$ |
$2$ |
$0$ |
2.180.4, 3.8640.8 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(7.223967\) |
\(1.203994\) |
$[40,45,555,6]$ |
$[240,1320,-2560,-589200,373248]$ |
$[6400000/3,440000/9,-32000/81]$ |
$y^2 + x^3y = -2$ |
| 20736.j.373248.1 |
20736.j |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{6} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(8.411823\) |
\(1.401971\) |
$[94,678,15328,-6]$ |
$[564,-3018,21596,767955,-373248]$ |
$[-458690014/3,52222969/36,-11926391/648]$ |
$y^2 + y = 2x^5 + x^4 - 5x^3 + 7x^2 - 4x + 1$ |
| 20736.k.373248.1 |
20736.k |
\( 2^{8} \cdot 3^{4} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\mathsf{CM})\) |
\(\Q \times \Q\) |
✓ |
$D_{2,1}$ |
|
|
|
$C_2^2$ |
$C_3:D_4$ |
$6$ |
$0$ |
2.180.4, 3.8640.8 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.326617\) |
\(12.512277\) |
\(1.362242\) |
$[40,45,555,6]$ |
$[240,1320,-2560,-589200,373248]$ |
$[6400000/3,440000/9,-32000/81]$ |
$y^2 + x^3y = 2$ |
| 20736.l.373248.1 |
20736.l |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{6} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathsf{QM}\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.480.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(18.600159\) |
\(1.033342\) |
$[146,738,29472,6]$ |
$[876,14262,207364,-5438445,373248]$ |
$[4146143186/3,924693409/36,276260689/648]$ |
$y^2 + y = 6x^5 + 9x^4 - x^3 - 3x^2$ |
| 20736.m.373248.1 |
20736.m |
\( 2^{8} \cdot 3^{4} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.40.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.138251\) |
\(9.538553\) |
\(1.318711\) |
$[64,57,979,6]$ |
$[384,4776,89024,2843760,373248]$ |
$[67108864/3,6520832/9,2848768/81]$ |
$y^2 + x^3y = x^5 + 4x^4 + 6x^3 + 7x^2 + 4x + 2$ |
| 20736.n.373248.1 |
20736.n |
\( 2^{8} \cdot 3^{4} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1$ |
$2$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(0.690794\) |
\(12.683765\) |
\(0.876187\) |
$[370,-14,-2312,-6]$ |
$[2220,205686,25563204,3610895571,-373248]$ |
$[-433399731250/3,-24117159625/4,-24302796025/72]$ |
$y^2 + y = 6x^5 - 9x^4 - 3x^3 + 4x^2 + 2x$ |
| 20736.o.995328.1 |
20736.o |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{5} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.074592\) |
\(6.704716\) |
\(1.000242\) |
$[372,2898,384570,124416]$ |
$[372,3834,-23036,-5817237,995328]$ |
$[28629151/4,6345483/32,-5534399/1728]$ |
$y^2 + (x^3 + x^2)y = x^4 + x^3 - 3$ |
